In general, internal combustion engines are controlled such that before an amount of NOx occlusion of a NOx storage reduction catalyst (hereinafter referred to as a NOx catalyst) arranged in an exhaust passage reaches a critical value, the flow rate of intake air is reduced and fuel is added to the exhaust passage, whereby the NOx occluded in the NOx catalyst is released and reduced, thus recovering the NOx occlusion capacity of the NOx catalyst. Such control is called NOx reduction processing.
In Japanese patent application laid-open No. 2002-38939, there is disclosed a technique in which when fuel is added in NOx reduction processing, etc., the flow rate of an exhaust gas, the temperature thereof, and the temperature of an inner wall of an exhaust passage are detected or estimated, so that an amount of evaporation of the added fuel (i.e., an amount of fuel atomization) is estimated based on these parameters, and the amount and timing of fuel addition are decided in consideration of the evaporation amount.
In addition, in Japanese patent application laid-open No. H9-228869, there is disclosed a technique in which when an internal combustion engine is operated with a rich air fuel ratio for a specific cylinder and a lean air fuel ratio for the other cylinders, the width of a fuel injection pulse for the rich cylinder is divided into a plurality of segments so that a spray of fuel having large particle sizes in an initial period of fuel injection is supplied to generate a lot of HC and CO to decrease the degree of richness of a mixture, thereby reducing a difference in output power between the rich cylinder and the lean cylinders.
In Japanese patent application laid-open No. 2001-41025, there is disclosed a technique in which during increase of a reducing agent supplied to a catalyst, which is disposed in an exhaust passage of an engine for reducing a NOx in an exhaust gas by means of the reducing agent, the increase of the reducing agent is temporarily suppressed when the degree of NOx reduction detected becomes a predetermined value or less.